Rudbeckia Hirta)* by Stanley G

252 GENETICS: STEPHENS AND BLAKESLEE PRoc. N. A. S.

corresponding to the heterogametic sex, to occur before fertilization, i.e., via the egg protoplasm) to be a widespread if not a universal type. Thus it is especially remarkable that we find the same situation again in D. melanogaster (table 3). The importance of such fadts for an understanding of the respective r6le of nucleus and!cytoplasm in development is obvious. * Actually I tried later to show that cytoplasmic inheritance might be preferable to that in the Y-chromosome. I have since shown (1942) why the original analysis must stand. Boycott, A. E., Diver, C., Garstang, S. L., and Turner, F. M., Phil. Trans. Roy. Soc. London, B219, 51-131 (1930). Goldschmidt, R., Ztschr. ind. Abst., 23, 1-199 (1920); Science, 95, 120-121 (1942). Goldschmidt, R., and Katsuki, K., Biol. Cenirbi., 47, 45-54 (1927); 48, 39-42, 685- 699 (1928); 51, 58-74 (1931). Pipkin, S.B., Genet., 32, 592-607 (1947). Sturtevant, A., Science, 58, 269-270 (1923); these PROCEEDINGS, 32, 84-87 (1946). Tanaka, Y., Genet., 9, 479-486 (1924). Toyama, K., Ztschr. ind. Abst., 1, 281-324 (1909); J. Gen., 2, 351-404 (1913).

PIGMENTS OF YELLOW-E YED RACES OF THE BLA CK-E YED SUSAN (RUDBECKIA HIRTA)* BY STANLEY G. STEPHENS AND ALBERT F. BLAKESLEE CARNEGIE INSTITUTION OF WASHINGTON, COLD SPRING HABOR, LONG ISLAND, AND SMI COLLEGE GENETICS EXPERIMENT STATION, NORTHAMPTON, MASSACHUSETTS, Read before the Academy, April 26, 1948 In. 1921 one1 of us reported on the breeding behavior of two genetically distinct types of yellow-coned plants in the Black-eyed Susan which nor- mally has cones with purple florets. It was shown that the two types, though phenotypically alike, could be separated into Black Yellows and Red Yellows by the fact that the cones of the former turn black when treated with alkali and those of the latter turn red when imilrly treated. The first of our Black Yellow plants came from open pollinated.seed from a purple-coned plant collected from the wild in the neighborhood of Storrs, Conn., in 1910. No Black Yellow plant had been found in nature since then until this past summer when a single yellow-coned plant was discotered at Saratoga Springs which by later test proved to be a Black Yellow. Red Yellows had been earlier found in two localities near Storrs. In one, about a mile from the University of Connecticut, only a single plant was observed. In the other locality, 6 or 7 miles away, several Red Yellows were found within an area of not over an acre. Since these are the only wild yellow- Downloaded by guest on October 6, 2021 VOL. 34, 1948 , GENETICS: STEPHENS AND BLAKESLEE 253

coned plants observed by the second author who for over 35 years has been interested in looking at fields of Rudbeckia, it can be concluded that yellow-coned types are extremely rare in nature. So far as we are aware the present case was the first in which a sharp chemical distinction could be established between the genetic groups within a phenotype, although, theoretically, all complementary types should differ chemically. The discovery of a reagent which would distinguish the two genetic types was made by testing out a considerable numiber of chemicals at random without any kn6wledge of the chemical process that might be involved. It is now possible to say something as to the chemical basis of the tests which were established empirically about 30 years ago. The chemical tests reported in the present preliminary paper were made by the first author (S.) with florets of the Black Yellow plant found in Sara- toga Springs and with those of Red Yellow plants which had segregated out of our horticultural types of tetraploid Black-eyed Susans. The sap-soluble pigments of plants fall into two main groups (a) anthoxanthins (flavones and flavonols, yellow or cream in color) and (b) anthocyanins which are red, purple or blue. The two groups are easily separated, since the anthoxanthins are soluble, anthocyanins insoluble in Ethyl Ace- tate. The crude pigments are extracted from the flowers by grinding in dilute (1 per cent) HCI and filtering. The clear filtrate is- then shaken re- peatedly with Ethyl Acetate, and thereby separated into two fractions, an E. A. fraction containing any anthoxanthins present, and an aqueous fraction which contains anthocyanins or leuco-anthocyanins (i.e., colorless anthocyanin precursors). The two fractions may then be subjected to various colorimetric tests which have been summarized by Scott-Moncrieff.2 Black Yellow Type from Saratoga Springs.-With conc. (8N) KOH 'gave black color (Black Yellow type). A portion of untreated cone was extracted with 1 per cent HCI and the filtrate exhaustively extracted with Ethyl Acetate. (Three successive shakings with equal bulk of Ethyl Ace- tate.) (a) Ethyl Acetate Fraction.-On evaporation to dryness on a water bath, a very small residue, creamy white in color, was obtained which when taken up in a small quantity of alcohol gave an almost colorless solution. On addition of a few drops of 1 per cent KOH a deep golden color was produced showing that an anthoxanthin was present. (b) Aqueozs Fraction.-This was quite colorless and gave no color reaction with dilute KOH. On boiling, with conc. HCI however, a deep purple red color was developed, showing that an anthocyanin precursor (leuco-anthocyanin) was present. Red Yellow Type (Tetraploid) from Garden Culture.-With conc. (8N) KOH gave red color (Red Yellow type). (a) Ethyl Acetate Fraction.-This contained an anthoxanthin and in Downloaded by guest on October 6, 2021 254 GENETICS: STEPHENS AND BLAKESLEE PRoc. N. A. S.

rather larger quantities than in the corresponding fraction from the Black Yellow type. (b) Aqueous Fraction.-This was colorless and developed no red color on boiling with conc. HCl. There was therefore no leuco-anthocyanin present. Purple Cone Type (Tetraploid) from Garden Culture.-(a) Ethyl Acetate Fraction.-This was identical with the corresponding fraction from the Red Yellow and Black Yellow types, i.e., an anthoxanthin giving a golden yellow color with dilute KOH but possibly in rather smaller quantities. (b) Aqueous Fraction.-This had a magenta color due to the presence of an anthocyanin. Anthocyanins occur in the plant in combination with various sugar radicles, i.e., as glycosides. A quick method is available2 for de- termining the nature of the glycosides, depending on their partition between two solvents, water and iso-amyl alcohol. On shaking an aqueous solution of the anthocyanin under test with iso-amyl alcohol it may be classified in one of three groups: (1) Monoglycosides.-The anthocyanin is distributed between the aqueous and alcoholic layers, and on dilution with water the concentration of the pigment in the alcoholic layer is increased. On saturating with NaCl the pigment is almost entirely taken up by the alcoholic layer. (2) Pentose Glycosides.-On diluting with water the concentration of the pigment in the alcoholic layer is decreased, but on saturating with NaCl nearly all the pigment passes into the alcoholic layer. (3) Diglycosides and Biosides.-Very little pigment is taken up by the alcoholic layer and its distribution is but slightly altered on dilution with water or on saturation with NaCl. The anthocyanin of Rudbeckia belongs in this class. Anthocyanins give specific color reactions with various reagents, and can be differentiated on this basis according to Robinson's method (summarized Scott-Moncrieff2). The anthocyanin from Rudbeckia gave the color reactions which are summarized as follows: Sium Sodium Sodium Ferric acetate carbonate hydroxide chloride Violet Violet-blue Pure blue Purplish-blue This combination of color reactions is characteristic of 3-glycosides of cyanidin (i.e., cyanidin in which the hydroxyl at position 3 in the pyran ring is replaced by a sugar molecule). The combined evidence from color reactions and partition between aqueous and iso-amyl alcohol solvents suggests that the pigment is probably cyanidin 3-bioside. To confirm this it wiU be necessary to examine the hfdrolyzed pigment spectrophoto- metrically and compare its absorption with the known spectral absorption Downloaded by guest on October 6, 2021 VOL. 34, 1948 GENETICS: STEPHENS AND BLAKESLEE 255

of cyanidin, and to determine the nature of the sugar residue by standard chemical methods. Miscellaneous Observations.-There is a suggestion that the Purple and Black Yellow types which &ontain an anthocyanin and a leuco-anthocyanin, respectively, contain less anthoxanthin than the Red Yellow types. This would be in accordance with general experience in other genera where a negative correlation between anthocyanin and anthoxanthin concentration has been established, leading to the hypothesis3-4 that both classes of pigments are derived from a common precursor, which is produced in rather limited quantity. In the present case the evidence is not critical since the flower types examined differ in chromosome number, and probably are con- siderably differentiated genetically as well. The nature of the anthoxanthin pigment cannot be determined without chemical analysis of larger amounts of material than were used in the present studies since small scale qualitative tests, such as have been developed for anthocyanin determination, are not available. However, since the anthoxanthin extract did not yield an anthocyanin pigment on reduction with zinc and hydrochloric acid, it probably does not contain glycosides of quercetin, which can be reduced to cyanidin under these conditions. A Chemical Explanation ofthe "Black Yellow" and "Red Yellow" Reactions with Strong Alkali.-Red Yellow cones were macerated in 8N KOH. The calyces developed a deep orange-red color, and the extract was orange. On acidifying with conc. HCI, the color was discharged. On adding Basic Lead Acetate and boiling, a deep orange precipitate was obtained-a characteristic reaction of anthoxanthins. It is clear that the orange-red color obtained on treating Red Yellow cones with strong alkali is due to the anthoxanthin previously found to be present in the Ethyl Acetate fraction described earlier in this paper. The orange-red color is merely due to the extreme concentration of the anthoxanthin in the calyces of the disc florets; the extract is orange or yellow in color depending on the dilution. Black Yellow cones yielded a greenish yetlow extract on grinding with 8N KOH. This was probably due to a mixture of anthoxanthin (orange- red) and leuco-anthocyanin which had been partially converted to anthocyanin (blue in alkaline solution). Continued grinding failed to leach out any darker pigment, and the color of the calyces faded showing that the pigment was being removed, but the extract remained greenish yellow. Pre- vious experience5 with certain flower types in Gossypium which contain a leuco-anthocyanin but no anthocyanin, had shown that under certain conditions of extraction the leuco-anthocyanin was unstable, and that when extracts were made by boiling the petals with 1 per cent HCI, the leuco- anthocyanin was partially converted to an anthocyanin, since the extracts gave green colors with alkalies changing to pink on re-acidifying. On the Downloaded by guest on October 6, 2021 256 GENETICS: STEPHENS AND BLAKESLEE PROC. N. A. S.

basis of this previous experience the Black Yellow cone was extracted by boiling with 1 per cent HCI. The extract was cooled and a few drops of strong KOH added. A green color was immediately produced, i.e., the extract behaved as if it contained a mixture of anthoxanthin (yellow) and anthocyanin (blue) pigments. On standing, the blue color faded leaving the golden yellow color characteristic of the anthoxanthin. When the alkaline solution with a green color was acidified by adding conc. HCI drop by drop, the green color turned to pink which also was unstable on standing. A pink color would be expected for an acid solution containing a mixture of anthoxanthin (colorless) and anthocyanin (red). Why the anthocyanin produced from the leuco-anthocyanin should be stable in the plant tissues but unstable on extraction is not known. It seems clear, however, that the black color produced by treating the cones with strong alkali is due to the superposition of orange-red (from the anthoxanthin) on blue (from the converted leuco-anthocyanin), and is therefore in conformity with the pigments obtained in the 1 per cent HCI extracts described earlier. Conlusions.-The Black Yellow type of Rudbeckia is able to produce a leuco-anthocyanin which is concentrated in the central cone of the flower. Cones of the Red Yellow types do not contain a leuco-anthocyanin, but presumably this type carries a gene which is able to convert the leuco-anthocyanin, as the genetic combination, Black Yellow/Red Yellow, is phenotypically purple-coned and contains an anthocyanin. The anthocyanincon- cerned is probably-subject to confirmation by more detailed methods-a bioside of cyanidin. Our tests show that there is more than a single gene controlling cone color in Rudbeckia. They also give some indications of the chemical steps involved in the formation of the purple pigment. The dominant allele (RY) of the red-yellow gene controls an essential chemical step in the gene reactions leading to the production of the leuco-anthocyanin. The dominant allele (BY) of the black-yellow gene controls a later step which converts the leuco-anthocyanin to an anthocyanin and its action is therefore dependent on the presence of (RY). When the latter is absent, the production of both leuco-anthocyanin and anthocyanin in the flower-cone is blocked. On this basis, it would be expected that the double recessive in a 9 : 3: 4 ratio of an F2 between black-yellow (by) and red-yellow (ry) would react as red- yellows. This appears to be the case. Our earlier records' show 158 purple-coned plants to 97 with yellow cones in an F2 population, which is close to the expected 9: 7 rati6. By the use of KOH the yellow-coned types were resolved into 43 by to 52 ry. The expectation on a 3:4 ratio is 40.7:54.3: 13.25. The agreement is close since the deviation is less than the probable error. The accompanying diagrams may help in an understanding of the re- lationships between the different cone colors. Downloaded by guest on October 6, 2021 VOL. 34, 1948 GENETICS: STEPHENS AND BLAKESLEE 257

Red Yellow Red Yellow Black Yellow Purple Normal (double recessive) ryry byby ryry ByBy RyRy byby RyRy ByBy cannot produce leuco- cannot produce leuco- has leuco-anthocyanin Produces both anthocyanin anthocyanin cannot produce antho- leuco- and an- cyanin thocyanin

RY BY Anthoxanthin - Leuco ---Anthocyanin ry blocks this reaction by blocks this reaction producing Red Yellows producing Black Yellows

It seems likely that the chemical mechanism described in this paper, whereby two acyanic mutant flower types produce a cyanic "normal" type in combination, may be of rather general occurrence. Superficially similar cases have been reported in Lathyrus,6 Antirrhinum7 and Cheiranthus,2 and it would be of interest to know whether in these genera also, one of each pair of complementary acyanic flower types contains a leuco-anthocyanin. In Gossypium a very similar case has recently been examined5 in which, as in Rudbeckia, one acyanic flower type carries a gene controlling the presence of a leuco-anthocyanin, and its complementary acyanic type a gene which converts the leuco-anthocyanin to an anthocyanin. Furthermore, unpub- lished studies have showni that the leuco-anthocyanin in Gossypium is in- timately related not only to the anthocyanin but also to the anthoxanthin pigments, since its spectral absorption is identical with that of the colorless intermediate reduction product obtained on reducing the anthoxanthin, quercetin, to the anthocyan pigment, cyanidin, in vitro. Apart from its intrinsic genetic interest, therefore, it is probable that a continued study of these and similar complementary acyanic flower mutants may lead to the discovery of other blocks in the syntheses of anthocyanins and anthoxanthins and so yield much valuable information on the natural interrelation of these pigments in the plant. Summary.-The following flower cone types are known in Rudbecki4a hirta: Purple (BY R Y), Black Yellow (by R Y), so-caUed because florets turn black in strong alkali, and Red Yellow (B Y ry and by ry), which turn red in alkali. Chemical studies of the pigments involved have shown that Purple Cone contains an anthocyan pigment, cyanidin; Black Yellow a leuco-anthocyanin convertible to cyanidin in vitro; and Red Yellow contains neither leuco-anthocyanin nor cyanidin. The flower cones of all types contain a yellow anthoxanthin pigment. Genetic and chemical find- ings are consistent with the hypothesis that the gene, R Y, is responsible for the production of the leuco-anthocyanin, and the geie, B Y, for its further conversion to cyanidin. The first step is blocked when R Y is replaced by ry, and the second step is blocked when B Y is replaced by by. Downloaded by guest on October 6, 2021 258 MA THEMA TICS: HUA AND VANDIVER PROC. N. A. S.

* Contribution from the Department of Botany, Smith College, New Series, No. 26. 1 Blakeslee, A. F., Zeitschr, ind. Vererb., 25, 211-221 (1921). 2Scott-Moncrieff, R., J. Genet., 32, 117-170 (1936). 3 Robinson, R., Nature (London), 137, 172-173 (19'36). 4Lawrence, W. J. C., and Price, J. R., Biol. Rev., 15, 35-58 (1940). 6 Stephens, S. G., Genetics (in press). * Bateson, W., Saunders, E. R., and Punnett, R. C., Proc. Roy. Soc. London, 77B, 236-238 (1905). 7 Wheldale, M., The Anthocyanin Pigments of Plants, Cambridge University Press, 1916.

ON THE EXISTENCE OF SOLUTIONS OF CERTAIN EQUATIONS IN A FINITE FIELD By L. K. HUA AND H. S. VANDIVER INSTITUTE FOR ADVANCED STUDY, PRINCETON, NEw JERSEY, AND DEPARTMENT OF APPLIED MATHEMATICS, UNIVERSITY oF TEtXAS Communicated April 7, 1948 In another paper' one of the authors stated that he had arrived at limits, both inferior and superior, for the number of solutions of the equation CiXll + C2X2G2 + ... + C.X'a. + C$+, = 0 (1)

in the x's where a's are integers such that0 < a < pn - 1; s> 2 forc,,+ I 0 and s > 2 for c5+ = 0, the c's being given element' of a finite field of order p, p prime, which will be designated by F(pn); and C, ... co, ... *XX8 0. (2) As a consequence of this result, one can obtain THEOREM I. The equation (1) with the restriction (2) always has at least k solutions in the x's for k any given positive integer provded pI' exceeds a certain limit. In this paper we shall give two quite different approaches to establish this theorem. The first is closely related to the one previously mentioned and the other argument, although subject to the limitation s > 2 when c.,+, $ 0, is far simpler and is based on a methodla which was introduced by one of the authors in the study of generalized Gaussian sums over a finite field. The limit given here can be sharpened, and the proof of this will be published later. Elsewhere2 it wasshown that the exact number of solutions of (1) may be determined directly if we know the exact number of solutions of 0"a, Om#. of the equation Downloaded by guest on October 6, 2021